New York Learning Standards Mathematics, Science, and...

New York Learning Standards Mathematics, Science, and Technology Standard 1: Analysis, Inquiry, and Design

Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.

Standard 2: Information Systems Students will access, generate, process, and transfer information using appropriate technologies.

Standard 3: Mathematics Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real- world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.

Standard 4: Science Students will understand and apply scientific concepts, principles, and theories pertaining to the physical setting and living environment and recognize the historical development of ideas in science.

Standard 5: Technology Students will apply technological knowledge and skills to design, construct, use, and evaluate products and systems to satisfy human and environmental needs.

Standard 6: Interconnectedness: Common Themes Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.

Standard 7: Interdisciplinary Problem Solving Students will apply the knowledge and thinking skills of mathematics, science, and technology to address real- life problems and make informed decisions.

1. Abstraction and symbolic representation are used tocommunicate mathematically.

Students:• use special mathematical notation and symbolism to

communicate in mathematics and to compare anddescribe quantities, express relationships, and relatemathematics to their immediate environments.

This is evident, for example, when students:

▲ describe their ages as an inequality such as 7 < ❒ < 10.

2. Deductive and inductive reasoning are used toreach mathematical conclusions.

Students:• use simple logical reasoning to develop conclusions,

recognizing that patterns and relationships present inthe environment assist them in reaching theseconclusions.

3. Critical thinking skills are used in the solution ofmathematical problems.

Students:• explore and solve problems generated from school, home,

and community situations, using concrete objects ormanipulative materials when possible.

1. The central purpose of scientific inquiry is todevelop explanations of natural phenomena in acontinuing, creative process.

Students:• ask “why” questions in attempts to seek greater

understanding concerning objects and events they haveobserved and heard about.

• question the explanations they hear from others andread about, seeking clarification and comparing themwith their own observations and understandings.

• develop relationships among observations to constructdescriptions of objects and events and to form their owntentative explanations of what they have observed.


▲ observe a variety of objects that either sink or float when placed in acontainer of water.* Working in groups, they propose an explanationof why objects sink or float. After sharing and discussing theirproposed explanation, they refine it and submit it for assessment.The explanation is rated on clarity and plausibility.

2. Beyond the use of reasoning and consensus,scientific inquiry involves the testing of proposedexplanations involving the use of conventionaltechniques and procedures and usually requiringconsiderable ingenuity.

Students:• develop written plans for exploring phenomena or for

evaluating explanations guided by questions or proposedexplanations they have helped formulate.

• share their research plans with others and revise thembased on their suggestions.

• carry out their plans for exploring phenomena throughdirect observation and through the use of simpleinstruments that permit measurements of quantities(e.g., length, mass, volume, temperature, and time).


▲ are asked to develop a way of testing their explanation of whyobjects sink or float when placed in a container of water.* Theytell what procedures and materials they will use and indicatewhat results will support their explanation. Their plan iscritiqued by others, they revise it, and submit it for assessment.The plan is rated on clarity, soundness in addressing the issue,and feasibility. After the teacher suggests modifications, theplan is carried out.

Standard 1—Analysis, Inquiry, and DesignElementary

Mathematical Analysis Scientific Inquiry

2

Key ideas are identified by numbers (1).Performance indicators are identified by bullets (•).

Sample tasks are identified by triangles (▲).

3. The observations made while testing proposedexplanations, when analyzed using conventional andinvented methods, provide new insights intophenomena.

Students:• organize observations and measurements of objects and

events through classification and the preparation ofsimple charts and tables.

• interpret organized observations and measurements,recognizing simple patterns, sequences, andrelationships.

• share their findings with others and actively seek theirinterpretations and ideas.

• adjust their explanations and understandings of objectsand events based on their findings and new ideas.


▲ prepare tables or other representations of their observations andlook for evidence which supports or refutes their explanation ofwhy objects sink or float when placed in a container of water.*After sharing and discussing their results with other groups,they prepare a brief research report that includes methods,findings, and conclusions. The report is rated on its clarity, carein carrying out the plan, and presentation of evidencesupporting the conclusions.

1. Engineering design is an iterative process involvingmodeling and optimization finding the best solutionwithin given constraints which is used to developtechnological solutions to problems within givenconstraints.

Students engage in the following steps in a design process:• describe objects, imaginary or real, that might be

modeled or made differently and suggest ways in whichthe objects can be changed, fixed, or improved.

• investigate prior solutions and ideas from books,magazines, family, friends, neighbors, and communitymembers.

• generate ideas for possible solutions, individually andthrough group activity; apply age-appropriatemathematics and science skills; evaluate the ideas anddetermine the best solution; and explain reasons for thechoices.

• plan and build, under supervision, a model of thesolution using familiar materials, processes, and handtools.

• discuss how best to test the solution; perform the testunder teacher supervision; record and portray resultsthrough numerical and graphic means; discuss orallywhy things worked or didn’t work; and summarizeresults in writing, suggesting ways to make the solutionbetter.


▲ read a story called Humpty’s Big Day wherein the readers visitthe place where Humpty Dumpty had his accident, and areasked to design and model a way to get to the top of the walland down again safely.

▲ generate, draw, and model ideas for a space station thatincludes a pleasant living and working environment.

▲ design and model footwear that they could use to walk on a cold,sandy surface.

Students will use mathematical analysis, scientific inquiry, and engineering design,as appropriate, to pose questions, seek answers, and develop solutions.

Engineering Design

3

* A variety of content-specific items can be substituted forthe italicized text

1. Information technology is used to retrieve, process,and communicate information and as a tool toenhance learning.

Students:• use a variety of equipment and software packages to

enter, process, display, and communicate information indifferent forms using text, tables, pictures, and sound.

• telecommunicate a message to a distant location withteacher help.

• access needed information from printed media,electronic data bases, and community resources.


▲ use the newspaper or magazine index in a library to findinformation on a particular topic.

▲ invite local experts to the school to share their expertise.

2. Knowledge of the impacts and limitations ofinformation systems is essential to its effective andethical use.

Students:• describe the uses of information systems in homes,

schools, and businesses.• understand that computers are used to store personal

information.• demonstrate ability to evaluate information.


▲ look for differences among species of bugs collected on the schoolgrounds, and classify them according to preferred habitat.

Standard 2—Information SystemsElementary

Information Systems

8



3. Information technology can have positive andnegative impacts on society, depending upon how it isused.

Students:• describe the uses of information systems in homes and

schools.• demonstrate ability to evaluate information critically.

Students will access, generate, process, and transfer information using appropriatetechnologies.

9

1. Students use mathematical reasoning to analyzemathematical situations, make conjectures, gatherevidence, and construct an argument.

Students:• use models, facts, and relationships to draw conclusions

about mathematics and explain their thinking.• use patterns and relationships to analyze mathematical

situations.• justify their answers and solution processes.• use logical reasoning to reach simple conclusions.


▲ build geometric figures out of straws.▲ find patterns in sequences of numbers, such as the triangular

numbers 1, 3, 6, 10, . . . .▲ explore number relationships with a calculator (e.g., 12 + 6 = 18,

11 + 7 = 18, etc.) and draw conclusions.

2. Students use number sense and numeration todevelop an understanding of the multiple uses ofnumbers in the real world, the use of numbers tocommunicate mathematically, and the use of numbersin the development of mathematical ideas.

Students:• use whole numbers and fractions to identify locations,

quantify groups of objects, and measure distances.• use concrete materials to model numbers and number

relationships for whole numbers and common fractions,including decimal fractions.

• relate counting to grouping and to place-value.• recognize the order of whole numbers and commonly

used fractions and decimals.• demonstrate the concept of percent through problems

related to actual situations.


▲ count out 15 small cubes and exchange ten of the cubes for a rodten cubes long.

▲ use the number line to show the position of 1/4.▲ figure the tax on $4.00 knowing that taxes are 7 cents per $1.00.

Standard 3—MathematicsElementary

Mathematical Reasoning Number and Numeration

14



Sample Problems

3. Students use mathematical operations andrelationships among them to understand mathematics.

Students:• add, subtract, multiply, and divide whole numbers.• develop strategies for selecting the appropriate

computational and operational method in problem-solving situations.

• know single digit addition, subtraction, multiplication,and division facts.

• understand the commutative and associative properties.


▲ use the fact that multiplication is commutative (e.g., 2 x 7 = 7 x 2), to assist them with their memorizing of thebasic facts.

▲ solve multiple-step problems that require at least two differentoperations.

▲ progress from base ten blocks to concrete models and then topaper and pencil algorithms.

4. Students use mathematical modeling/multiplerepresentation to provide a means of presenting,interpreting, communicating, and connectingmathematical information and relationships.

Students:• use concrete materials to model spatial relationships.• construct tables, charts, and graphs to display and

analyze real-world data.• use multiple representations (simulations, manipulative

materials, pictures, and diagrams) as tools to explain theoperation of everyday procedures.

• use variables such as height, weight, and hand size topredict changes over time.

• use physical materials, pictures, and diagrams to explainmathematical ideas and processes and to demonstrategeometric concepts.


▲ build a 3 x 3 x 3 cube out of blocks.▲ use square tiles to model various rectangles with an area of 24

square units.▲ read a bar graph of population trends and write an explanation

of the information it contains.

Students will understand mathematics and become mathematically confident bycommunicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study ofnumber systems, geometry, algebra, data analysis, probability, and trigonometry.

Operations Modeling/MultipleRepresentation

15

Sample Problems

5. Students use measurement in both metric andEnglish measure to provide a major link between theabstractions of mathematics and the real world inorder to describe and compare objects and data.

Students:• understand that measurement is approximate, never

exact.• select appropriate standard and nonstandard

measurement tools in measurement activities.• understand the attributes of area, length, capacity,

weight, volume, time, temperature, and angle.• estimate and find measures such as length, perimeter,

area, and volume using both nonstandard and standardunits.

• collect and display data.• use statistical methods such as graphs, tables, and charts

to interpret data.


▲ measure with paper clips or finger width.▲ estimate, then calculate, how much paint would be needed to

cover one wall.▲ create a chart to display the results of a survey conducted

among the classes in the school, or graph the amounts of surveyresponses by grade level.

6. Students use ideas of uncertainty to illustrate thatmathematics involves more than exactness whendealing with everyday situations.

Students:• make estimates to compare to actual results of both

formal and informal measurement.• make estimates to compare to actual results of

computations.• recognize situations where only an estimate is required.• develop a wide variety of estimation skills and strategies.• determine the reasonableness of results.• predict experimental probabilities.• make predictions using unbiased random samples.• determine probabilities of simple events.


▲ estimate the length of the room before measuring.▲ predict the average number of red candies in a bag before

opening a group of bags, counting the candies, and thenaveraging the number that were red.

▲ determine the probability of picking an even numbered slip froma hat containing slips of paper numbered 1, 2, 3, 4, 5, and 6.

Standard 3—MathematicsElementary

Measurement Uncertainty

16



Sample Problems

7. Students use patterns and functions to developmathematical power, appreciate the true beauty ofmathematics, and construct generalizations thatdescribe patterns simply and efficiently.

Students:• recognize, describe, extend, and create a wide variety of

patterns.• represent and describe mathematical relationships.• explore and express relationships using variables and

open sentences.• solve for an unknown using manipulative materials.• use a variety of manipulative materials and technologies

to explore patterns.• interpret graphs.• explore and develop relationships among two- and three-

dimensional geometric shapes.• discover patterns in nature, art, music, and literature.


▲ represent three more than a number is equal to nine as n + 3 = 9.

▲ draw leaves, simple wallpaper patterns, or write numbersequences to illustrate recurring patterns.

▲ write generalizations or conclusions from display data in chartsor graphs.

Students will understand mathematics and become mathematically confident bycommunicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study ofnumber systems, geometry, algebra, data analysis, probability, and trigonometry.

Patterns/Functions

17

Sample Problem

1. The Earth and celestial phenomena can be describedby principles of relative motion and perspective.

Students:• describe patterns of daily, monthly, and seasonal changes

in their environment.


▲ conduct a long-term weather investigation, such as running aweather station or collecting weather data.

▲ keep a journal of the phases of the moon over a one-monthperiod. This information is collected for several different one-month periods and compared.

2. Many of the phenomena that we observe on Earthinvolve interactions among components of air, water,and land.

Students:• describe the relationships among air, water, and land on

Earth.


▲ observe a puddle of water outdoors after a rainstorm. On areturn visit after the puddle has disappeared, students describewhere the water came from and possible locations for it now.

▲ assemble rock and mineral collections based on characteristicssuch as erosional features or crystal size features.

3. Matter is made up of particles whose propertiesdetermine the observable characteristics of matterand its reactivity.

Students:• observe and describe properties of materials using

appropriate tools.• describe chemical and physical changes, including

changes in states of matter.


▲ compare the appearance of materials when seen with andwithout the aid of a magnifying glass.

▲ investigate simple physical and chemical reactions and thechemistry of household products, e.g., freezing, melting, andevaporating; a comparison of new and rusty nails; the role ofbaking soda in cooking.

4. Energy exists in many forms, and when these formschange energy is conserved.

Students:• describe a variety of forms of energy (e.g., heat, chemical,

light) and the changes that occur in objects when theyinteract with those forms of energy.

• observe the way one form of energy can be transformedinto another form of energy present in commonsituations (e.g., mechanical to heat energy, mechanical toelectrical energy, chemical to heat energy).


▲ investigate the interactions of liquids and powders that result inchemical reactions (e.g., vinegar and baking soda) compared tointeractions that do not (e.g., water and sugar).

▲ in order to demonstrate the transformation of chemical toelectrical energy, construct electrical cells from objects, such aslemons or potatoes, using pennies and aluminum foil inserted inslits at each end of fruits or vegetables; the penny andaluminum are attached by wires to a milliammeter. Studentscan compare the success of a variety of these electrical cells.

5. Energy and matter interact through forces thatresult in changes in motion.

Students:• describe the effects of common forces (pushes and pulls)

on objects, such as those caused by gravity, magnetism,and mechanical forces.

• describe how forces can operate across distances.


▲ investigate simple machines and use them to perform tasks.

Standard 4—ScienceElementary

Physical Setting

30



1. Living things are both similar to and different fromeach other and nonliving things.

Students:• describe the characteristics of and variations between

living and nonliving things.• describe the life processes common to all living things.


▲ grow a plant or observe a pet, investigating what it requires tostay alive, including evaluating the relative importance andnecessity of each item.

▲ investigate differences in personal body characteristics, such astemperature, pulse, heart rate, blood pressure, and reactiontime.

2. Organisms inherit genetic information in a varietyof ways that result in continuity of structure andfunction between parents and offspring.

Students:• recognize that traits of living things are both inherited

and acquired or learned.• recognize that for humans and other living things there

is genetic continuity between generations.


▲ interact with a classroom pet, observe its behaviors, and recordwhat they are able to teach the animal, such as navigation of amaze or performance of tricks, compared to that which remainsconstant, such as eye color, or number of digits on anappendage.

▲ use breeding records and photographs of racing horses orpedigreed animals to recognize that variations exist fromgeneration to generation but “like begets like.”

3. Individual organisms and species change over time.

Students:• describe how the structures of plants and animals

complement the environment of the plant or animal. • observe that differences within a species may give

individuals an advantage in surviving and reproducing.


▲ relate physical characteristics of organisms to habitatcharacteristics (e.g., long hair and fur color change for mammalsliving in cold climates).

▲ visit a farm or a zoo and make a written or pictorial comparisonof members of a litter and identify characteristics that mayprovide an advantage.

4. The continuity of life is sustained throughreproduction and development.

Students:• describe the major stages in the life cycles of selected

plants and animals.• describe evidence of growth, repair, and maintenance, such

as nails, hair, and bone, and the healing of cuts and bruises.

This is evident, for example, when students:▲ grow bean plants or butterflies; record and describe stages of

development.

5. Organisms maintain a dynamic equilibrium thatsustains life.

Students:• describe basic life functions of common living specimens

(guppy, mealworm, gerbil).• describe some survival behaviors of common living specimens.• describe the factors that help promote good health and

growth in humans.

This is evident, for example, when students:▲ observe a single organism over a period of weeks and describe

such life functions as moving, eating, resting, and eliminating.▲ observe and demonstrate reflexes such as pupil dilation and

contraction and relate such reflexes to improved survival.▲ analyze the extent to which diet and exercise habits meet

cardiovascular, energy, and nutrient requirements.

6. Plants and animals depend on each other and theirphysical environment.

Students:• describe how plants and animals, including humans,

depend upon each other and the nonliving environment. • describe the relationship of the sun as an energy source

for living and nonliving cycles.

This is evident, for example, when students:▲ investigate how humans depend on their environment

(neighborhood), by observing, recording, and discussing theinteractions that occur in carrying out their everyday lives.

▲ observe the effects of sunlight on growth for a garden vegetable.

7. Human decisions and activities have had a profoundimpact on the physical and living environment.

Students:• identify ways in which humans have changed their

environment and the effects of those changes.

This is evident, for example, when students:▲ give examples of how inventions and innovations have changed

the environment; describe benefits and burdens of thosechanges.

Students will understand and apply scientific concepts, principles, and theoriespertaining to the physical setting and living environment and recognize thehistorical development of ideas in science.

The Living Environment

31

1. Engineering design is an iterative process involvingmodeling and optimization used to developtechnological solutions to problems within givenconstraints.

Students:• describe objects, imaginary or real, that might be

modeled or made differently and suggest ways in whichthe objects can be changed, fixed, or improved.

• investigate prior solutions and ideas from books,magazines, family, friends, neighbors, and communitymembers.

• generate ideas for possible solutions, individually andthrough group activity; apply age-appropriate mathemat-ics and science skills; evaluate the ideas and determinethe best solution; and explain reasons for the choices.

• plan and build, under supervision, a model of thesolution using familiar materials, processes, and handtools.

• discuss how best to test the solution; perform the testunder teacher supervision; record and portray resultsthrough numerical and graphic means; discuss orallywhy things worked or didn’t work; and summarizeresults in writing, suggesting ways to make the solutionbetter.


▲ read a story called Humpty’s Big Day wherein the readers visitthe place where Humpty Dumpty had his accident, and areasked to design and model a way to get to the top of the walland down again safely.

▲ generate and draw ideas for a space station that includes apleasant living and working environment.

▲ design and model footwear that they could use to walk on a cold,sandy surface.

2. Technological tools, materials, and other resourcesshould be selected on the basis of safety, cost,availability, appropriateness, and environmentalimpact; technological processes change energy,information, and material resources into more usefulforms.

Students:• explore, use, and process a variety of materials and

energy sources to design and construct things.• understand the importance of safety, cost, ease of use,

and availability in selecting tools and resources for aspecific purpose.

• develop basic skill in the use of hand tools. • use simple manufacturing processes (e.g., assembly, mul-

tiple stages of production, quality control) to produce aproduct.

• use appropriate graphic and electronic tools andtechniques to process information.


▲ explore and use materials, joining them with the use ofadhesives and mechanical fasteners to make a cardboard mari-onette with moving parts.

▲ explore materials and use forming processes to heat and bendplastic into a shape that can hold napkins.

▲ explore energy sources by making a simple motor that useselectrical energy to produce continuous mechanical motion.

▲ develop skill with a variety of hand tools and use them to makeor fix things.

▲ process information electronically such as using a video systemto advertise a product or service.

▲ process information graphically such as taking photos anddeveloping and printing the pictures.

Standard 5—TechnologyElementary

Engineering Design

36

Tools, Resources, and TechnologicalProcesses



3. Computers, as tools for design, modeling,information processing, communication, and systemcontrol, have greatly increased human productivityand knowledge.

Students:• identify and describe the function of the major

components of a computer system.• use the computer as a tool for generating and drawing

ideas.• control computerized devices and systems through

programming.• model and simulate the design of a complex environment

by giving direct commands.


▲ control the operation of a toy or household appliance byprogramming it to perform a task.

▲ execute a computer program, such as SimCity, Theme Park, orThe Factory to model and simulate an environment.

▲ model and simulate a system using construction modelingsoftware, such as The Incredible Machine.

4. Technological systems are designed to achieve spe-cific results and produce outputs, such as products,structures, services, energy, or other systems.

Students:• identify familiar examples of technological systems that

are used to satisfy human needs and wants, and selectthem on the basis of safety, cost, and function.

• assemble and operate simple technological systems,including those with interconnecting mechanisms toachieve different kinds of movement.

• understand that larger systems are made up of smallercomponent subsystems.


▲ assemble and operate a system made up from a battery, switch,and doorbell connected in a series circuit.

▲ assemble a system with interconnecting mechanisms, such as ajack-in-the-box that pops up from a box with a hinged lid.

▲ model a community-based transportation system which includessubsystems such as roadways, rails, vehicles, and trafficcontrols.

Students will apply technological knowledge and skills to design, construct, use, andevaluate products and systems to satisfy human and environmental needs.

Computer Technology Technological Systems

37

Sample Problem/Activity

Computer design formodel community

5. Technology has been the driving force in theevolution of society from an agricultural to anindustrial to an information base.

Students:• identify technological developments that have

significantly accelerated human progress.


▲ construct a model of an historical or future-orientedtechnological device or system and describe how it hascontributed or might contribute to human progress.

▲ make a technological timeline in the form of a hanging mobile oftechnological devices.

▲ model a variety of timekeeping devices that reflect historicaland modern methods of keeping time.

▲ make a display contrasting early devices or tools with theirmodern counterparts.

6. Technology can have positive and negative impactson individuals, society, and the environment andhumans have the capability and responsibility toconstrain or promote technological development.

Students:• describe how technology can have positive and negative

effects on the environment and on the way people liveand work.


▲ handmake an item and then participate in a line productionexperience where a quantity of the item is mass produced;compare the benefits and disadvantages of mass production andcraft production.

▲ describe through example, how familiar technologies (includingcomputers) can have positive and negative impacts on theenvironment and on the way people live and work.

▲ identify the pros and cons of several possible packagingmaterials for a student-made product.

Standard 5—TechnologyElementary

History and Evolution of Technology Impacts of Technology

38




7. Project management is essential to ensuring thattechnological endeavors are profitable and thatproducts and systems are of high quality and builtsafely, on schedule, and within budget.

Students:• participate in small group projects and in structured

group tasks requiring planning, financing, production,quality control, and follow-up.

• speculate on and model possible technological solutionsthat can improve the safety and quality of the school orcommunity environment.


▲ help a group to plan and implement a school project or activity,such as a school picnic or a fund-raising event.

▲ plan as a group, division of tasks and construction steps neededto build a simple model of a structure or vehicle.

▲ redesign the work area in their classroom with an eye towardimproving safety.

Students will apply technological knowledge and skills to design, construct, use, andevaluate products and systems to satisfy human and environmental needs.

Management of Technology

39


HOW CAN WE REDUCESOLID WASTE

IN OUR SCHOOL?

EvaluationStudents will be able to develop and implement usefulsolid waste reduction strategies within their schoolbased upon their investigations of the current solidwaste stream.

1. Through systems thinking, people can recognize thecommonalities that exist among all systems and howparts of a system interrelate and combine to performspecific functions.

Students:• observe and describe interactions among components of

simple systems.• identify common things that can be considered to be

systems (e.g., a plant population, a subway system,human beings).

2. Models are simplified representations of objects,structures, or systems used in analysis, explanation,interpretation, or design.

Students:• analyze, construct, and operate models in order to

discover attributes of the real thing.• discover that a model of something is different from the

real thing but can be used to study the real thing.• use different types of models, such as graphs, sketches,

diagrams, and maps, to represent various aspects of thereal world.


▲ compare toy cars with real automobiles in terms of size andfunction.

▲ model structures with building blocks.▲ design and construct a working model of the human circulatory

system to explore how varying pumping pressure might affectblood flow.

▲ describe the limitations of model cars, planes, or houses.▲ use model vehicles or structures to illustrate how the real object

functions.▲ use a road map to determine distances between towns and

cities.

Standard 6—Interconnectedness:Common Themes Elementary

Systems Thinking Models

48




Students will understand the relationships and common themes that connectmathematics, science, and technology and apply the themes to these and other areasof learning.

Magnitude and Scale Equilibrium and Stability

49


3. The grouping of magnitudes of size, time, frequency,and pressures or other units of measurement into aseries of relative order provides a useful way to dealwith the immense range and the changes in scale thataffect the behavior and design of systems.

Students:• provide examples of natural and manufactured things

that belong to the same category yet have very differentsizes, weights, ages, speeds, and other measurements.

• identify the biggest and the smallest values as well as theaverage value of a system when given information aboutits characteristics and behavior.


▲ compare the weight of small and large animals.▲ compare the speed of bicycles, cars, and planes.▲ compare the life spans of insects and trees.▲ collect and analyze data related to the height of the students in

their class, identifying the tallest, the shortest, and the averageheight.

▲ compare the annual temperature range of their locality.

4. Equilibrium is a state of stability due either to alack of changes (static equilibrium) or a balancebetween opposing forces (dynamic equilibrium).

Students:• cite examples of systems in which some features stay the

same while other features change.• distinguish between reasons for stability—from lack of

changes to changes that counterbalance one another tochanges within cycles.


▲ record their body temperatures in different weather conditionsand observe that the temperature of a healthy human beingstays almost constant even though the external temperaturechanges.

▲ identify the reasons for the changing amount of fresh water in areservoir and determine how a constant supply is maintained.

5. Identifying patterns of change is necessary formaking predictions about future behavior andconditions.

Students:• use simple instruments to measure such quantities as

distance, size, and weight and look for patterns in thedata.

• analyze data by making tables and graphs and lookingfor patterns of change.


▲ compare shoe size with the height of people to determine if thereis a trend.

▲ collect data on the speed of balls rolling down ramps of differentslopes and determine the relationship between speed andsteepness of the ramp.

▲ take data they have collected and generate tables and graphs tobegin the search for patterns of change.

6. In order to arrive at the best solution that meetscriteria within constraints, it is often necessary tomake trade-offs.

Students:• determine the criteria and constraints of a simple

decision making problem.• use simple quantitative methods, such as ratios, to

compare costs to benefits of a decision problem.


▲ describe the criteria (e.g., size, color, model) and constraints(e.g., budget) used to select the best bicycle to buy.

▲ compare the cost of cereal to number of servings to figure out thebest buy.

Standard 6—Interconnectedness:Common Themes Elementary

Patterns of Change Optimization

50




Students will understand the relationships and common themes that connectmathematics, science, and technology and apply the themes to these and other areasof learning.

51


1. The knowledge and skills of mathematics, science,and technology are used together to make informeddecisions and solve problems, especially those relatingto issues of science/technology/society, consumerdecision making, design, and inquiry into phenomena.

Students:• analyze science/technology/society problems and issues

that affect their home, school, orcommunity, and carryout a remedial course of action.

• make informed consumer decisions by applyingknowledge about the attributes of particular productsand making cost/benefit tradeoffs to arrive at an optimalchoice.

• design solutions to problems involving a familiar andreal context, investigate related science concepts toinform the solution, and use mathematics to model,quantify, measure, and compute.

• observe phenomena and evaluate them scientifically andmathematically by conducting a fair test of the effect ofvariables and using mathematical knowledge andtechnological tools to collect, analyze, and present dataand conclusions.


▲ develop and implement a plan to reduce water or energyconsumption in their home.

▲ choose paper towels based on tests of absorption quality,strength, and cost per sheet.

▲ design a wheeled vehicle, sketch and develop plans, testdifferent wheel and axle designs to reduce friction, chart results,and produce a working model with correct measurements.

▲ collect leaves of similar size from different varieties of trees, andcompare the ratios of length to width in order to determinetwhether the ratios are the same for all species.

2. Solving interdisciplinary problems involves avariety of skills and strategies, including effectivework habits; gathering and processing information;generating and analyzing ideas; realizing ideas; mak-ing connections among the common themes ofmathematics, science, and technology; and presentingresults.

Students participate in an extended, culminatingmathematics, science, and technology project. The projectwould require students to:

• work effectively• gather and process information• generate and analyze ideas• observe common themes• realize ideas• present results

This is evident, for example, when students, addressing the issue ofsolid waste at the school in an interdisciplinaryscience/technology/society project:

▲ use the newspaper index to find out about how solid waste ishandled in their community, and interview the custodial staff tocollect data about how much solid waste is generated in theschool, and they make and use tables and graphs to look forpatterns of change. Students work together to reach consensuson the need for recycling and on choosing a material to recycle—in this case, paper.

▲ investigate the types of paper that could be recycled, measurethe amount (weight, volume) of this type of paper in their schoolduring a one-week period, and calculate the cost. Studentsinvestigate the processes involved in changing used paper into auseable product and how and why those changes work as theydo.

▲ using simple mixers, wire screens, and lint, leaves, rags, etc.,students recycle used paper into useable sheets and evaluatethe quality of the product. They present their results usingcharts, graphs, illustrations, and photographs to the principaland custodial staff.

Standard 7—Interdisciplinary Problem Solving Elementary

Connections Strategies

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Working Effectively: Contributing to the work of a brainstorming group, laboratory partnership, cooperative learning group, orproject team; planning procedures; identify and managing responsibilities of team members; and staying on task, whether workingalone or as part of a group.

Gathering and Processing Information: Accessing information from printed media, electronic data bases, and communityresources and using the information to develop a definition of the problem and to research possible solutions.

Generating and Analyzing Ideas: Developing ideas for proposed solutions, investigating ideas, collecting data, and showingrelationships and patterns in the data.

Common Themes: Observing examples of common unifying themes, applying them to the problem, and using them to betterunderstand the dimensions of the problem.

Realizing Ideas: Constructing components or models, arriving at a solution, and evaluating the result.

Presenting Results: Using a variety of media to present the solution and to communicate the results.

Students will apply the knowledge and thinking skills of mathematics, science, andtechnology to address real-life problems and make informed decisions.

Skills and Strategies for Interdisciplinary Problem Solving

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New York Learning Standards Mathematics, Science, and...

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